853 resultados para large effective population size
Resumo:
Fruit drop can cause major yield losses in Australian lychee orchards, the severity varying with cultivar and season. Research in China, South Africa and Israel has demonstrated the potential for synthetic auxins used as foliar sprays to reduce fruit drop in lychee. Trials tested the efficacy of the synthetic auxin 3-5-6 trichloro-2-phridyl-oxyacetic acid (TPA) applied as a foliar spray at 50 ppm on fruit drop and fruit size on the cultivars ‘Fay Zee Siu’, ‘Kaimana’, ‘Kwai Mai Pink’, ‘Souey Tung’ and ‘Tai So’. TPA reduced fruit drop when applied to fruit greater than 12 mm in length but increased fruit drop when fruit were smaller. Fruit size at the time of application had less effect on the response than the level of natural fruit drop. When natural fruit drop was high, TPA significantly reduced it; by up to 18.7 in ‘Fay Zee Siu’, 37.1 in ‘Kaimana’, 39.8 in ‘Kwai Mai Pink’, 15.1 in ‘Souey Tung’ and 7.7 in ‘Tai So’. TPA was less effective when natural fruit drop was low. TPA increased the number of large fruit and frequently increased the number of small fruit at harvest. The small fruit were associated with an increase in the retention of fruit with poorly developed (chicken tongue) seed. Average fruit size was generally larger (up to 12.7 in ‘Souey Tung’ and 22 in ‘Tai So’) with TPA applications.
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The knowledge about the optimal rearing conditions, such as water temperature and quality, photoperiod and density, with the understanding of animal nutritional requirements forms the basis of economically stable aquaculture for freshwater crayfish. However, the shift from a natural environment to effective culture conditions induces several changes, not only at the population level, but also at the individual level. The social contacts between conspecifics increase with increasing animal density. The competition for limited resources (e.g. food, shelter, mates) is more severe with the presence of agonistic behaviour and may lead to unequal distribution of these. The objectives of this study were to: 1) study the distribution of a common food resource between communally reared signal crayfish (Pacifastacus leniusculus) and to assign potential feeding hierarchy on the basis of individual food intake measurements, 2) explore the possibilities of size distribution manipulations to affect population dynamics and food intake to improve growth and survival in culture and 3) study the effect of food ration and spatial distribution on food intake and to explore the effect of temperature and food ration on growth and body composition of freshwater crayfish. The feeding ranks between animals were assigned with a new method for individual food intake measurement of communally reared crayfish. This technique has a high feasibility and a great potential to be applied in crayfish aquaculture studies. In this study, signal crayfish showed high size-related variability in food consumption both among individuals within a group (inter-individual) and within individual day-to-day variation (intra-individual). Increased competition for food led to an unequal distribution of this resource and this may be a reason for large growth differences between animals. The consumption was significantly higher when reared individually in comparison with communal housing. These results suggest that communally housed crayfish form a feeding hierarchy and that the animal size is the major factor controlling the position in this hierarchy. The optimisation of the social environment ( social conditions ) was evaluated in this study as a new approach to crayfish aquaculture. The results showed that the absence of conspecifics (individual rearing vs. communal housing) affects growth rate, food intake and the proportion of injured animals, whereas size variation between animals influences the number and duration of agonistic encounters. In addition, animal size had a strong influence on the fighting success of signal crayfish reared in a social milieu with a wide size variation of conspecifics. Larger individuals initiated and won most of the competitions, which suggests size-based social hierarchy of P. leniusculus. This is further supported by the fact that the length and weight gain of smaller animals increased after size grading, maybe because of a better access to the food resource due to diminished social pressure. However, the high dominance index was not based on size under conditions of limited size variation, e.g. those characteristic of restocked natural populations and aquaculture, indicating the important role of behaviour on social hierarchy.
Resumo:
Spatial and temporal variation in the abundance of species can often be ascribed to spatial and temporal variation in the surrounding environment. Knowledge of how biotic and abiotic factors operate over different spatial and temporal scales in determining distribution, abundance, and structure of populations lies at the heart of ecology. The major part of the current ecological theory stems from studies carried out in central parts of the distributional range of species, whereas knowledge of how marginal populations function is inadequate. Understanding how marginal populations, living at the edge of their range, function is however in a key position to advance ecology and evolutionary biology as scientific disciplines. My thesis focuses on the factors affecting dynamics of marginal populations of blue mussels (Mytilus edulis) living close to their tolerance limits with regard to salinity. The thesis aims to highlight the dynamics at the edge of the range and contrast these with dynamics in more central parts of the range in order to understand the potential interplay between the central and the marginal part in the focal system. The objectives of the thesis are approached by studies on: (1) factors affecting regional patterns of the species, (2) long-term temporal dynamics of the focal species spaced along a regional salinity gradient, (3) selective predation by increasing populations of roach (Rutilus rutilus) when feeding on their main food item, the blue mussel, (4) the primary and secondary effects of local wave exposure gradients and (5) the role of small-scale habitat heterogeneity as determinants of large-scale pattern. The thesis shows that populations of blue mussels are largely determined by large scale changes in sea water salinity, affecting mainly recruitment success and longevity of local populations. In opposite to the traditional view, the thesis strongly indicate that vertebrate predators strongly affect abundance and size structure of blue mussel populations, and that the role of these predators increases towards the margin where populations are increasingly top-down controlled. The thesis also indicates that the positive role of biogenic habitat modifiers increases towards the marginal areas, where populations of blue mussels are largely recruitment limited. Finally, the thesis shows that local blue mussel populations are strongly dependent on high water turbulence, and therefore, dense populations are constrained to offshore habitats. Finally, the thesis suggests that ongoing sedimentation of rocky shores is detrimental for the species, affecting recruitment success and post-recruit survival, pushing stable mussel beds towards offshore areas. Ongoing large scale changes in the Baltic Sea, especially dilution processes with attendant effects, are predicted to substantially contract the distributional range of the mussel, but also affect more central populations. The thesis shows that in order to understand the functioning of marginal populations, research should (1) strive for multi-scale approaches in order to link ecosystem patterns with ecosystem processes, and (2) challenge the prevailing tenets that origin from research carried out in central areas that may not be valid at the edge.
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The Capercaillie (Tetrao urogallus L.) is often used as a focal species for landscape ecological studies: the minimum size for its lekking area is 300 ha, and the annual home range for an individual may cover 30 80 km2. In Finland, Capercaillie populations have decreased by approximately 40 85%, with the declines likely to have started in the 1940s. Although the declines have partly stabilized from the 1990s onwards, it is obvious that the negative population trend was at least partly caused by changes in human land use. The aim of this thesis was to study the connections between human land use and Capercaillie populations in Finland, using several spatial and temporal scales. First, the effect of forest age structure on Capercaillie population trends was studied in 18 forestry board districts in Finland, during 1965 1988. Second, the abundances of Capercaillie and Moose (Alces alces L.) were compared in terms of several land-use variables on a scale of 50 × 50 km grids and in five regions in Finland. Third, the effects of forest cover and fine-grain forest fragmentation on Capercaillie lekking area persistence were studied in three study locations in Finland, on 1000 and 3000 m spatial scales surrounding the leks. The analyses considering lekking areas were performed with two definitions for forest: > 60 and > 152 m3ha 1 of timber volume. The results show that patterns and processes at large spatial scales strongly influence Capercaillie in Finland. In particular, in southwestern and eastern Finland, high forest cover and low human impact were found to be beneficial for this species. Forest cover (> 60 m3ha 1 of timber) surrounding the lekking sites positively affected lekking area persistence only at the larger landscape scale (3000 m radius). The effects of older forest classes were hard to assess due to scarcity of older forests in several study areas. Young and middle-aged forest classes were common in the vicinity of areas with high Capercaillie abundances especially in northern Finland. The increase in the amount of younger forest classes did not provide a good explanation for Capercaillie population decline in 1965 1988. In addition, there was no significant connection between mature forests (> 152 m3ha 1 of timber) and lekking area persistence in Finland. It seems that in present-day Finnish landscapes, area covered with old forest is either too scarce to efficiently explain the abundance of Capercaillie and the persistence of the lekking areas, or the effect of forest age is only important when considering smaller spatial scales than the ones studied in this thesis. In conclusion, larger spatial scales should be considered for assessing the future Capercaillie management. According to the proposed multi-level planning, the first priority should be to secure the large, regional-scale forest cover, and the second priority should be to maintain fine-grained, heterogeneous structure within the separate forest patches. A management unit covering hundreds of hectares, or even tens or hundreds of square kilometers, should be covered, which requires regional-level land-use planning and co-operation between forest owners.
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The European aspen (Populus tremula) is a keystone species for biodiversity in boreal forests. However, the future of aspen may be threatened, because large aspens have mostly been removed from managed forests, whereas regeneration and the long-term persistence of mature trees are subjects of concern in protected areas. Aspen is a pioneer tree, and it can reproduce both sexually by seed and asexually by root suckers. Through asexual reproduction aspen forms clones, groups of genetically identical trees (ramets). In my thesis, I have studied the structure of aspen populations in terms of number, size, clonal and demographic properties. Additionally, I have investigated the emergence and survival of seedlings as well as the seed quantity and quality in crosses between the European and hybrid aspen. To study the regeneration and population structure, mature aspens were recorded in old-growth and managed forests in eastern Finland based on a large-scale inventory (11 400 ha). In addition, small aspen trees were surveyed on sample plots. Clonal structure was investigated both by morphological characters and by DNA-based markers (microsatellites). Seedling emergence and survival was studied with two sowing experiments. With crosses between European and hybrid aspens we wanted to study whether elevated temperatures due to climate change would benefit the different crosses of European and hybrid aspen unequally and thus affect the gene flow between the two species. The average volumes of mature aspen were 5.3 m3/ha in continuous old-growth, and 0.8 m3/ha in managed forests. Results indicate also that large aspen trees in managed forests are a legacy of the past less intensively managed forest landscapes. Long-term persistence of aspen in protected areas can only be secured by restoration measures creating sufficiently large gaps for regeneration. More emphasis should be given to sparing aspens in thinnings and to retaining of mature aspens in regeneration cutting in managed forests. Aspen was found to be spatially aggregated in the landscape. This could be explained by site type, disturbance history and / or limitations in seed dispersal. Clonal structure does not explain the spatial aggregation, since average size of the clones was only 2.3 ramets, and most clones (70 %) consisted of just one ramet. The small size of the clones suggests that most of them are relatively young. Therefore, sexual reproduction may be more common than has previously been thought. Seedling emergence was most successful in mineral soil especially, when the site had been burned. Only few seedlings occurred on humus. Survival of the seedlings was low, and strongly dependent on moisture, but also on seedbed conditions. The seeds were found to maintain their germinability longer than has earlier been thought to be possible. Interspecific crosses produced more seeds with higher quality than intraspecific crosses. When temperature was elevated, germination of hybrid aspen seeds increased more than seeds from P. tremula x P. tremula crosses. These results suggest that hybrid aspen may have a significant genetic impact on the European aspen, and this effect may become strengthened by climate warming.
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Background Risk-stratification of diffuse large B-cell lymphoma (DLBCL) requires identification of patients with disease that is not cured despite initial R-CHOP. Although the prognostic importance of the tumour microenvironment (TME) is established, the optimal strategy to quantify it is unknown. Methods The relationship between immune-effector and inhibitory (checkpoint) genes was assessed by NanoString™ in 252 paraffin-embedded DLBCL tissues. A model to quantify net anti-tumoural immunity as an outcome predictor was tested in 158 R-CHOP treated patients, and validated in tissue/blood from two independent R-CHOP treated cohorts of 233 and 140 patients respectively. Findings T and NK-cell immune-effector molecule expression correlated with tumour associated macrophage and PD-1/PD-L1 axis markers consistent with malignant B-cells triggering a dynamic checkpoint response to adapt to and evade immune-surveillance. A tree-based survival model was performed to test if immune-effector to checkpoint ratios were prognostic. The CD4*CD8:(CD163/CD68)*PD-L1 ratio was better able to stratify overall survival than any single or combination of immune markers, distinguishing groups with disparate 4-year survivals (92% versus 47%). The immune ratio was independent of and added to the revised international prognostic index (R-IPI) and cell-of-origin (COO). Tissue findings were validated in 233 DLBCL R-CHOP treated patients. Furthermore, within the blood of 140 R-CHOP treated patients immune-effector:checkpoint ratios were associated with differential interim-PET/CT+ve/-ve expression.
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Uveal melanoma is the most common primary intraocular malignancy in adults. Vision in the affected eye is threatened by both the tumor and side-effects from the treatments currently available. Poor prognosis for saving vision increases with tumor size and, consequently, enucleation has been the treatment of choice for large uveal melanomas in most centers. However, increasing evidence suggests that no survival benefit is gained (nor lost) by enucleation as compared to eye-conserving methods. The Helsinki University Eye Hospital has since 1990 offered episcleral iodine-125 plaque brachytherapy (IBT) for all patients unwilling to undergo enucleation for a large uveal melanoma. The primary aim of this study was to assess survival, local tumor recurrence and preservation of the eye and vision after IBT in a population-based series of 97 patients with uveal melanomas classified as large by the Collaborative Ocular Melanoma Study (COMS) criteria. Further aims included reporting the incidence of side-effects and assessing the role of intraocular dose distribution and clinical risk factors in their development. Finally, means to improve the current treatment were investigated by using computer models to compare existing plaques with collimating ones and by comparing the outcome of a subgroup of 54 IBT patients with very thick tumors with 33 patients with similarly-sized tumors managed with transscleral local resection (TSR) in Liverpool, United Kingdom. Kaplan-Meier estimates of all-cause and melanoma-specific survival at 5 years after IBT were 62% and 65%, respectively, and visually comparable with the survival experience of patients reported after enucleation by the COMS. Local recurrence developed in 6% of eyes and 84% of eyes were conserved at 5 years. Visual prognosis was guarded with 11% avoiding loss of 20/70 vision and 26% avoiding loss of 20/400 vision in the tumor eye at 2 years. Large tumor height and short distance from the posterior pole were independently associated with loss of vision. Using cumulative incidence analysis to account for competing risks, such as enucleation and metastatic death, the 5-year incidence of cataract after IBT was 79%, glaucoma 60%, optic neuropathy 46%, maculopathy 52%, persistent or recurring retinal detachment (RD) 25%, and vitreous hemorrhage 36%. In multivariate competing risks regression models, increasing tumor height was associated with cataract, iris neovascularization and RD. Maculopathy and optic neuropathy were associated with distance from the tumor to the respective structure. Median doses to the tumor apex, macula and optic disc were 81 Gy (range, 40-158), 79 Gy (range, 12-632), and 83 Gy (range, 10-377), respectively. Dose to the optic disc was independently associated with optic neuropathy, and both dose to the optic disc and dose to the macula predicted vision loss after IBT. Simulated treatment using collimating plaques resulted in clinically meaningful reduction in both optic disc (median reduction, 30 Gy) and macular (median reduction, 36 Gy) doses as compared to the actual treatment with standard plaques. In the subgroup of patients with uveal melanomas classified as large because of tumor height, cumulative incidence analysis revealed that while long-term preservation of 20/70 vision was rare after both IBT and TSR, preservation of 20/400 vision was better after TSR (32% vs. 5% at 5 years). In multivariate logistic regression models, TSR was independently associated with better preservation of 20/400 vision (OR 0.03 at 2 years, P=0.005) No cases of secondary glaucoma were observed after TSR and optic neuropathy was rare. However, local tumor recurrence was more common after TSR than it was after IBT (Cumulative incidence 41% vs. 7% at 5 years, respectively). In terms of survival, IBT seems to be a safe alternative to enucleation in managing large uveal melanomas. Local tumor control is no worse than with medium-sized tumors and the chances of avoiding secondary enucleation are good. Unfortunately, side-effects from radiotherapy are frequent, especially in thick tumors, and long-term prognosis of saving vision is consequently guarded. Some complications can be limited by using collimating plaques and by managing uveal melanomas that are large because of tumor height with TSR instead of IBT. However, the patient must be willing to accept a substantial risk of local tumor recurrence after TSR and it is best suited for cases in which the preservation of vision in the tumor eye is critical.
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Cyclosporine is an immunosuppressant drug with a narrow therapeutic index and large variability in pharmacokinetics. To improve cyclosporine dose individualization in children, we used population pharmacokinetic modeling to study the effects of developmental, clinical, and genetic factors on cyclosporine pharmacokinetics in altogether 176 subjects (age range: 0.36–20.2 years) before and up to 16 years after renal transplantation. Pre-transplantation test doses of cyclosporine were given intravenously (3 mg/kg) and orally (10 mg/kg), on separate occasions, followed by blood sampling for 24 hours (n=175). After transplantation, in a total of 137 patients, cyclosporine concentration was quantified at trough, two hours post-dose, or with dose-interval curves. One-hundred-four of the studied patients were genotyped for 17 putatively functionally significant sequence variations in the ABCB1, SLCO1B1, ABCC2, CYP3A4, CYP3A5, and NR1I2 genes. Pharmacokinetic modeling was performed with the nonlinear mixed effects modeling computer program, NONMEM. A 3-compartment population pharmacokinetic model with first order absorption without lag-time was used to describe the data. The most important covariate affecting systemic clearance and distribution volume was allometrically scaled body weight i.e. body weight**3/4 for clearance and absolute body weight for volume of distribution. The clearance adjusted by absolute body weight declined with age and pre-pubertal children (< 8 years) had an approximately 25% higher clearance/body weight (L/h/kg) than did older children. Adjustment of clearance for allometric body weight removed its relationship to age after the first year of life. This finding is consistent with a gradual reduction in relative liver size towards adult values, and a relatively constant CYP3A content in the liver from about 6–12 months of age to adulthood. The other significant covariates affecting cyclosporine clearance and volume of distribution were hematocrit, plasma cholesterol, and serum creatinine, explaining up to 20%–30% of inter-individual differences before transplantation. After transplantation, their predictive role was smaller, as the variations in hematocrit, plasma cholesterol, and serum creatinine were also smaller. Before transplantation, no clinical or demographic covariates were found to affect oral bioavailability, and no systematic age-related changes in oral bioavailability were observed. After transplantation, older children receiving cyclosporine twice daily as the gelatine capsule microemulsion formulation had an about 1.25–1.3 times higher bioavailability than did the younger children receiving the liquid microemulsion formulation thrice daily. Moreover, cyclosporine oral bioavailability increased over 1.5-fold in the first month after transplantation, returning thereafter gradually to its initial value in 1–1.5 years. The largest cyclosporine doses were administered in the first 3–6 months after transplantation, and thereafter the single doses of cyclosporine were often smaller than 3 mg/kg. Thus, the results suggest that cyclosporine displays dose-dependent, saturable pre-systemic metabolism even at low single doses, whereas complete saturation of CYP3A4 and MDR1 (P-glycoprotein) renders cyclosporine pharmacokinetics dose-linear at higher doses. No significant associations were found between genetic polymorphisms and cyclosporine pharmacokinetics before transplantation in the whole population for which genetic data was available (n=104). However, in children older than eight years (n=22), heterozygous and homozygous carriers of the ABCB1 c.2677T or c.1236T alleles had an about 1.3 times or 1.6 times higher oral bioavailability, respectively, than did non-carriers. After transplantation, none of the ABCB1 SNPs or any other SNPs were found to be associated with cyclosporine clearance or oral bioavailability in the whole population, in the patients older than eight years, or in the patients younger than eight years. In the whole population, in those patients carrying the NR1I2 g.-25385C–g.-24381A–g.-205_-200GAGAAG–g.7635G–g.8055C haplotype, however, the bioavailability of cyclosporine was about one tenth lower, per allele, than in non-carriers. This effect was significant also in a subgroup of patients older than eight years. Furthermore, in patients carrying the NR1I2 g.-25385C–g.-24381A–g.-205_-200GAGAAG–g.7635G–g.8055T haplotype, the bioavailability was almost one fifth higher, per allele, than in non-carriers. It may be possible to improve individualization of cyclosporine dosing in children by accounting for the effects of developmental factors (body weight, liver size), time after transplantation, and cyclosporine dosing frequency/formulation. Further studies are required on the predictive value of genotyping for individualization of cyclosporine dosing in children.
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Diagnostic radiology represents the largest man-made contribution to population radiation doses in Europe. To be able to keep the diagnostic benefit versus radiation risk ratio as high as possible, it is important to understand the quantitative relationship between the patient radiation dose and the various factors which affect the dose, such as the scan parameters, scan mode, and patient size. Paediatric patients have a higher probability for late radiation effects, since longer life expectancy is combined with the higher radiation sensitivity of the developing organs. The experience with particular paediatric examinations may be very limited and paediatric acquisition protocols may not be optimised. The purpose of this thesis was to enhance and compare different dosimetric protocols, to promote the establishment of the paediatric diagnostic reference levels (DRLs), and to provide new data on patient doses for optimisation purposes in computed tomography (with new applications for dental imaging) and in paediatric radiography. Large variations in radiation exposure in paediatric skull, sinus, chest, pelvic and abdominal radiography examinations were discovered in patient dose surveys. There were variations between different hospitals and examination rooms, between different sized patients, and between imaging techniques; emphasising the need for harmonisation of the examination protocols. For computed tomography, a correction coefficient, which takes individual patient size into account in patient dosimetry, was created. The presented patient size correction method can be used for both adult and paediatric purposes. Dental cone beam CT scanners provided adequate image quality for dentomaxillofacial examinations while delivering considerably smaller effective doses to patient compared to the multi slice CT. However, large dose differences between cone beam CT scanners were not explained by differences in image quality, which indicated the lack of optimisation. For paediatric radiography, a graphical method was created for setting the diagnostic reference levels in chest examinations, and the DRLs were given as a function of patient projection thickness. Paediatric DRLs were also given for sinus radiography. The detailed information about the patient data, exposure parameters and procedures provided tools for reducing the patient doses in paediatric radiography. The mean tissue doses presented for paediatric radiography enabled future risk assessments to be done. The calculated effective doses can be used for comparing different diagnostic procedures, as well as for comparing the use of similar technologies and procedures in different hospitals and countries.
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The quantity of fruit consumed by dispersers is highly variable among individuals within plant populations. The outcome Of Such selection operated by firugivores has been examined mostly with respect to changing spatial contexts. The influence of varying temporal contexts on frugivore choice, and their possible demographic and evolutionary consequences is poorly understood. We examined if temporal variation in fruit availability across a hierarchy of nested temporal levels (interannual, intraseasonal, 120 h, 24 h) altered frugivore choice for a complex seed dispersal system in dry tropical forests of southern India. The interactions between Phyllanthus emblica and its primary disperser (ruminants) was mediated by another frugivore (a primate),which made large quantities of fruit available on the ground to ruminants. The direction and strength of crop size and neighborhood effects on this interaction varied with changing temporal contexts.Fruit availability was higher in the first of the two study years, and at the start of the season in both years. Fruit persistence on trees,determined by primate foraging, was influenced by crop size andconspecific neighborhood densities only in the high fruit availability year. Fruit removal by ruminants was influenced by crop size in both years and neighborhood densities only in the high availability year. In both years, these effects were stronger at the start of the season.Intraseasonal reduction in fruit availability diminished inequalities in fruit removal by ruminants and the influence of crop size and fruiting neighborhoods. All trees were not equally attractive to frugivores in a P. emblica population at all points of time. Temporal asymmetry in frugivore-mediated selection could reduce potential for co-evolution between firugivores and plants by diluting selective pressures. Inter-dependencies; formed between disparate animal consumers can add additional levels of complexity to plant-frugivore mutualistic networks and have potential reproductive consequences for specific individuals within populations.
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This communication describes the voltage‐current characteristics in the breakdown region of p‐n junctions made on polycrystalline silicon of large grain size. The observed soft breakdown characteristics have been explained by taking into account the effect of curvature of the junction near the grain boundaries.
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In an earlier study, we reported on the excitation of large-scale vortices in Cartesian hydrodynamical convection models subject to rapid enough rotation. In that study, the conditions for the onset of the instability were investigated in terms of the Reynolds (Re) and Coriolis (Co) numbers in models located at the stellar North pole. In this study, we extend our investigation to varying domain sizes, increasing stratification, and place the box at different latitudes. The effect of the increasing box size is to increase the sizes of the generated structures, so that the principal vortex always fills roughly half of the computational domain. The instability becomes stronger in the sense that the temperature anomaly and change in the radial velocity are observed to be enhanced. The model with the smallest box size is found to be stable against the instability, suggesting that a sufficient scale separation between the convective eddies and the scale of the domain is required for the instability to work. The instability can be seen upto the colatitude of 30 degrees, above which value the flow becomes dominated by other types of mean flows. The instability can also be seen in a model with larger stratification. Unlike the weakly stratified cases, the temperature anomaly caused by the vortex structures is seen to depend on depth.
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The growth and dissolution dynamics of nonequilibrium crystal size distributions (CSDs) can be determined by solving the governing population balance equations (PBEs) representing reversible addition or dissociation. New PBEs are considered that intrinsically incorporate growth dispersion and yield complete CSDs. We present two approaches to solving the PBEs, a moment method and a numerical scheme. The results of the numerical scheme agree with the moment technique, which can be solved exactly when powers on mass-dependent growth and dissolution rate coefficients are either zero or one. The numerical scheme is more general and can be applied when the powers of the rate coefficients are non-integers or greater than unity. The influence of the size dependent rates on the time variation of the CSDs indicates that as equilibrium is approached, the CSDs become narrow when the exponent on the growth rate is less than the exponent on the dissolution rate. If the exponent on the growth rate is greater than the exponent on the dissolution rate, then the polydispersity continues to broaden. The computation method applies for crystals large enough that interfacial stability issues, such as ripening, can be neglected. (C) 2002 Elsevier Science B.V. All rights reserved.
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The solution of a bivariate population balance equation (PBE) for aggregation of particles necessitates a large 2-d domain to be covered. A correspondingly large number of discretized equations for particle populations on pivots (representative sizes for bins) are solved, although at the end only a relatively small number of pivots are found to participate in the evolution process. In the present work, we initiate solution of the governing PBE on a small set of pivots that can represent the initial size distribution. New pivots are added to expand the computational domain in directions in which the evolving size distribution advances. A self-sufficient set of rules is developed to automate the addition of pivots, taken from an underlying X-grid formed by intersection of the lines of constant composition and constant particle mass. In order to test the robustness of the rule-set, simulations carried out with pivotwise expansion of X-grid are compared with those obtained using sufficiently large fixed X-grids for a number of composition independent and composition dependent aggregation kernels and initial conditions. The two techniques lead to identical predictions, with the former requiring only a fraction of the computational effort. The rule-set automatically reduces aggregation of particles of same composition to a 1-d problem. A midway change in the direction of expansion of domain, effected by the addition of particles of different mean composition, is captured correctly by the rule-set. The evolving shape of a computational domain carries with it the signature of the aggregation process, which can be insightful in complex and time dependent aggregation conditions. (c) 2012 Elsevier Ltd. All rights reserved.